Sphere and Dot Product Representations of Graphs
نویسندگان
چکیده
منابع مشابه
Dot Product Representations of Graphs
We introduce the concept of dot product representations of graphs, giving some motivations as well as surveying the previously known results. We extend these representations to more general fields, looking at the complex numbers, rational numbers, and finite fields. Finally, we study the behavior of dot product representations in field extensions.
متن کاملDot Product Representations of Planar Graphs
A graph G is a k-dot product graph if there exists a vector labelling u : V (G)→ Rk such that u(i)Tu(j) ≥ 1 if and only if ij ∈ E(G). Fiduccia, Scheinerman, Trenk and Zito [4] asked whether every planar graph is a 3-dot product graph. We show that the answer is “no”. On the other hand, every planar graph is a 4-dot product graph. We also answer the corresponding questions for planar graphs of p...
متن کاملWhat Graphs are 2-Dot Product Graphs?
From a set of d-dimensional vectors for some integer d ≥ 1, we obtain a d-dot product graph by letting each vector au correspond to a vertex u and by adding an edge between two vertices u and v if and only if their dot product au · av ≥ t, for some fixed, positive threshold t. Dot product graphs can be used to model social networks. To understand the position of d-dot product graphs in the land...
متن کاملDirected Random Dot Product Graphs
In this paper we consider three models for random graphs that utilize the inner product as their fundamental object. We analyze the behavior of these models with respect to clustering, the small world property, and degree distribution. These models are motivated by the random dot product graphs developed by Kraetzl, Nickel and Scheinerman. We extend their results to fully parameterize the condi...
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this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2012
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-012-9394-8